   In the unsupervised case, we know nothing about the data source, so we can only use reconstruction to constrain the representation. However, only reconstruction is not enough for disentanglement problem [1]}, so we try to use an unique representation prior distribution to guide the representation learning. We know that all disentanglement models of the VAE series match the posterior distribution \(q_{\phi }(z|x)\)  to standard normal distribution prior \(\mathcal {N}(0, I)\) , and they can get disentanglement representation in each dimension because of the independence across \(\mathcal {N}(0, I)\) . For meeting our neural block representation set, we set the prior distribution \(p(z)\)  as \(\mathcal {N}(0,\Sigma )\) , where \(\Sigma \)  is a block diagonal symmetric matrix. Of course, the dimension of each block corresponds to the segmentation of each hidden layer. In the unsupervised model, the target is reconstruction, so we can decompose Eq. (REF ) as:
\(\min &I(h^{i-1};s^i)-\beta I(s^i;x)\nonumber \\&\le \mathbb {E}_{p(h^{i-1})}[D_{KL}(q(z^i|h^{i-1})\Vert p(z))] \\&-D_{KL}(q_{\phi }(z^i)\Vert p(z))\\&-\beta [\mathbb {E}_{p(h^{i-1},y^i)}[\mathbb {E}_{q_{\phi }(s^i|h^{i-1})}[\log p_{\theta }(x|s^i)]]\\&-D_{KL}(q_{\phi }(z^{i-1})\Vert p_{D}(x))]\) 
